A proof of the generalized Nakayama conjecture for algebras with \(J^{2l+1}=0\) and \(A/J^ l\) representation finite
Let \(A\) be a finite dimensional algebra over a field \(k\). The generalized Nakayama conjecture states \(\text{Ext}_ A^ i (\Hom_ k(A,k),S)\neq 0\) for each simple \(A\)-module \(S\) and some \(i\geq 0\). A more general version is known if \(J(A)^ 3=0\) [\textit{E. L. Green} and \textit{B. Zimmermann- Huisgen}, Math. Z. 206, No. 4, 505-526 (1991; Zbl 0707.16002)]. Here the authors give a short proof under the assumption that there exists a natural number \(t\) such that \(J(A)^{2t+1}=0\) and \(A/J(A)^ t\) is representation finite.
scientific article; zbMATH DE number 60681